Recent activity
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commented on curve #4204
Specialization at T = -318/133 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where A4 = 1840758517133685517328T^8 - 28551969868039231295840T^7 - 1772998693252999313402080T^6 - 759387847760867496814400T^5 - 598922555435041558626640T^4 - 5448009866437772… -
submitted curve #4204 — rank ≥ 26, log |Δ| = 290.56
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commented on curve #4203
Specialization at T = 388/5 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where A4 = -2350796244229826784432T^8 + 40408811499609701188800T^7 - 807647185297995630241792T^6 + 1124780763822387162339456T^5 - 1304766910580579021664360T^4 + 14435396501706244… -
submitted curve #4203 — rank ≥ 26, log |Δ| = 293.20
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commented on curve #4202
Specialization at T = -511/37 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where A4 = -154503213541262535600T^8 + 4159635009352858651680T^7 - 21187086453270000393696T^6 - 687438318305734637863392T^5 - 4576470188855512350897360T^4 - 1932200428706742237… -
submitted curve #4202 — rank ≥ 24, log |Δ| = 271.38
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commented on curve #4201
Specialization at T = -11584/4313 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where A4 = -154503213541262535600T^8 + 4159635009352858651680T^7 - 21187086453270000393696T^6 - 687438318305734637863392T^5 - 4576470188855512350897360T^4 - 193220042870674… -
submitted curve #4201 — rank ≥ 26, log |Δ| = 318.27
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commented on curve #4200
Mestre rank-12 quartic family on locus sextuple [0,7,1182,1375,1382,1532] at T=391 (y^2=(g^2-p(x-T)p(x+T))/T^2, Jacobian); 18 independent points from a quartic rational-point search. -
submitted curve #4200 — rank ≥ 18, log |Δ| = 148.33
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submitted curve #4199 — rank ≥ 9, log |Δ| = 40.31
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commented on curve #4198
AI-assisted (Claude) search: Mestre-Nagao sieve over the universal Z/2xZ/4 family y^2 = x(x+a^2)(x+b^2) with (a,b) = (488395, 148148), then 2-descent (PARI ellrank, checked with mwrank). Rank exactly 7. -
submitted curve #4198 — rank ≥ 7, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 146.68 ☆ record for ℤ/2ℤ × ℤ/4ℤ torsion, rank ≥ 7: Faltings height
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commented on curve #4197
AI-assisted (Claude) search: Mestre-Nagao sieve over the universal Z/2xZ/4 family y^2 = x(x+a^2)(x+b^2) with (a,b) = (448324, 264607), then 2-descent (PARI ellrank, checked with mwrank). Rank exactly 7. -
submitted curve #4197 — rank ≥ 7, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 147.65 ☆ record for ℤ/2ℤ × ℤ/4ℤ torsion, rank ≥ 7: naive height
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recorded the primes of bad reduction of curve #4196 — rank ≥ 27, log |Δ| = 295.82
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commented on curve #4196
Specialization at T = -257/534 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where A4 = -4247232044073407555787T^8 + 31562440352380138911048T^7 - 1079699554459262036768544T^6 + 808673010384011405337504T^5 - 370492253920133220842280T^4 - 583074314969616… -
submitted curve #4196 — rank ≥ 27, log |Δ| = 295.82
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commented on curve #4195
Specialization at T = 5403/1139 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where A4 = -4247232044073407555787T^8 + 31562440352380138911048T^7 - 1079699554459262036768544T^6 + 808673010384011405337504T^5 - 370492253920133220842280T^4 - 58307431496961… -
submitted curve #4195 — rank ≥ 26, log |Δ| = 305.93
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recorded the primes of bad reduction of curve #4194 — rank ≥ 18, log |Δ| = 155.94
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commented on curve #4194
Mestre split-sextic roots (0, 13, 1568, 1581, 1700, 1756), primitive shift T=89/2. -
submitted curve #4194 — rank ≥ 18, log |Δ| = 155.94
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commented on curve #4193
Mestre rank-12 quartic family on locus sextuple [0,14,790,819,859,920] at T=491 (y^2=(g^2-p(x-T)p(x+T))/T^2, Jacobian); 18 independent points from a quartic rational-point search. -
submitted curve #4193 — rank ≥ 18, log |Δ| = 148.85
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commented on curve #4192
Specialization at T = -5938/5319 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where A4 = -4437370829345071269937785502500T^8 + 24731294533954602783634178920800T^7 - 24905343694917325040325875752236T^6 - 73371957550294374341624859203376T^5 + 1138813436… -
submitted curve #4192 — rank ≥ 24, log |Δ| = 253.42 ★ record for rank ≥ 24: conductor
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commented on curve #4191
Specialization at T = 57654/12097 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where A4 = -4437370829345071269937785502500T^8 + 24731294533954602783634178920800T^7 - 24905343694917325040325875752236T^6 - 73371957550294374341624859203376T^5 + 113881343… -
submitted curve #4191 — rank ≥ 27, log |Δ| = 292.64
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commented on curve #4190
Specialization at T = -373/1268 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where A4 = -73932522356183031905227T^8 + 649309903876882877687472T^7 - 1685916835628140824312084T^6 + 645581139407117375333216T^5 - 406054368862523371209330T^4 - 858600221311…